(6-x)(x+6)-(x-11)x=36

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Solution for (6-x)(x+6)-(x-11)x=36 equation: 


Simplifying
(6 + -1x)(x + 6) + -1(x + -11) * x = 36

Reorder the terms:
(6 + -1x)(6 + x) + -1(x + -11) * x = 36

Multiply (6 + -1x) * (6 + x)
(6(6 + x) + -1x * (6 + x)) + -1(x + -11) * x = 36
((6 * 6 + x * 6) + -1x * (6 + x)) + -1(x + -11) * x = 36
((36 + 6x) + -1x * (6 + x)) + -1(x + -11) * x = 36
(36 + 6x + (6 * -1x + x * -1x)) + -1(x + -11) * x = 36
(36 + 6x + (-6x + -1x2)) + -1(x + -11) * x = 36

Combine like terms: 6x + -6x = 0
(36 + 0 + -1x2) + -1(x + -11) * x = 36
(36 + -1x2) + -1(x + -11) * x = 36

Reorder the terms:
36 + -1x2 + -1(-11 + x) * x = 36

Reorder the terms for easier multiplication:
36 + -1x2 + -1x(-11 + x) = 36
36 + -1x2 + (-11 * -1x + x * -1x) = 36
36 + -1x2 + (11x + -1x2) = 36

Reorder the terms:
36 + 11x + -1x2 + -1x2 = 36

Combine like terms: -1x2 + -1x2 = -2x2
36 + 11x + -2x2 = 36

Add '-36' to each side of the equation.
36 + 11x + -36 + -2x2 = 36 + -36

Reorder the terms:
36 + -36 + 11x + -2x2 = 36 + -36

Combine like terms: 36 + -36 = 0
0 + 11x + -2x2 = 36 + -36
11x + -2x2 = 36 + -36

Combine like terms: 36 + -36 = 0
11x + -2x2 = 0

Solving
11x + -2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(11 + -2x) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying
x = 0

Subproblem 2
Set the factor '(11 + -2x)' equal to zero and attempt to solve:

Simplifying
11 + -2x = 0

Solving
11 + -2x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-11' to each side of the equation.
11 + -11 + -2x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -2x = 0 + -11
-2x = 0 + -11

Combine like terms: 0 + -11 = -11
-2x = -11

Divide each side by '-2'.
x = 5.5

Simplifying
x = 5.5
Solution
x = {0, 5.5}

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